On the last day of the IFCAM workshop in Bangalore, Marc Lavielle from INRIA presented a talk on mixed effects where he illustrated his original computer language Monolix. And mentioned that his CRC Press book on Mixed Effects Models for the Population Approach was out! (Appropriately listed as out on a 14th of July on amazon!) He actually demonstrated the abilities of Monolix live and on diabets data provided by an earlier speaker from Kolkata, which was a perfect way to start initiating a collaboration! Nice cover (which is all I saw from the book at this stage!) that maybe will induce candidates to write a review for CHANCE. Estimation of those mixed effect models relies on stochastic EM algorithms developed by Marc Lavielle and Éric Moulines in the 90’s, as well as MCMC methods.

As I am now back home after a rather lengthy and somewhat eventful trip [getting too early to Bangalore airport with 3 hours to spend in the nice and very quiet lounge, followed by another 5 hour wait in the very nice but no so quiet Bombay airport lounge, no visit to the cockpit this time!, and then the usual sick passenger blocking all trains from Paris-Charles de Gaulle airport for one hour, reaching home to find my 97-year old neighbour fallen in her kitchen and calling for help!], I cannot but reflect on the difference between my two trips to India, from the chaos of Varanasi to the orderly peace of the campus of the Indian Institute of Science of Bangalore and even to some extent of the whole city of Bangalore, all proportions guarded. Even managing to get a [new] pair of [new] prescription glasses (or rather spectacles) within three days!

I thus found this trip much less stressful and much profitable, from enjoying the local food to discussing with Indian statisticians. The purpose of the IFCAM workshop was to bring both groups together for potential joint projects funded by IFCAM (at the travel level). While I found most talks were driven by specific applications, esp. in genomics, there are directions where we could indeed collaborate, from capture-recapture to astrostatistics. So it may be that I’ll be back in India in a near future!

Second day at the Indo-French Centre for Applied Mathematics and the workshop. Maybe not the most exciting day in terms of talks (as I missed the first two plenary sessions by (a) oversleeping and (b) running across the campus!). However I had a neat talk with another conference participant that led to [what I think are] interesting questions… (And a very good meal in a local restaurant as the guest house had not booked me for dinner!)

To wit: given a target like

the simulation of λ can be demarginalised into the simulation of

where z is a latent (and artificial) variable. This means a Gibbs sampler simulating λ given z and z given λ can produce an outcome from the target (*). Interestingly, another completion is to consider that the zi‘s are U(0,yi) and to see the quantity

as an unbiased estimator of the target. What’s quite intriguing is that the quantity remains the same but with different motivations: (a) demarginalisation versus unbiasedness and (b) zi ∼ Exp(λ) versus zi ∼ U(0,yi). The stationary is the same, as shown by the graph below, the core distributions are [formally] the same, … but the reasoning deeply differs.

Obviously, since unbiased estimators of the likelihood can be justified by auxiliary variable arguments, this is not in fine a big surprise. Still, I had not thought of the analogy between demarginalisation and unbiased likelihood estimation previously. Continue reading →

First day at the Indo-French Centre for Applied Mathematics and the get-together (or speed-dating!) workshop. The campus of the Indian Institute of Science of Bangalore where we all stay is very pleasant with plenty of greenery in the middle of a very busy city. Plus, being at about 1000m means the temperature remains tolerable for me, to the point of letting me run in the morning.Plus, staying in a guest house in the campus also means genuine and enjoyable south Indian food.

The workshop is a mix of statisticians and of mathematicians of neurosciences, from both India and France, and we are few enough to have a lot of opportunities for discussion and potential joint projects. I gave the first talk this morning (hence a fairly short run!) on ABC model choice with random forests and, given the mixed audience, may have launched too quickly into the technicalities of the forests. Even though I think I kept the statisticians on-board for most of the talk. While the mathematical biology talks mostly went over my head (esp. when I could not resist dozing!), I enjoyed the presentation of Francis Bach of a fast stochastic gradient algorithm, where the stochastic average is only updated one term at a time, for apparently much faster convergence results. This is related with a joint work with Éric Moulines that both Éric and Francis presented in the past month. And makes me wonder at the intuition behind the major speed-up. Shrinkage to the mean maybe?